A. A. Abramov, V. I. Ul'yanova, L. F. Yukhno, “On certain properties of a nonlinear eigenvalue problem for Hamiltonian systems of ordinary differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 4,Pages <nobr>638

This article is cited in 7 papers

On certain properties of a nonlinear eigenvalue problem for Hamiltonian systems of ordinary differential equations

A. A. Abramov^a, V. I. Ul'yanova^a, L. F. Yukhno^b

^a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
^b Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia

Abstract: Properties of the eigenvalues are examined in a nonlinear self-adjoint eigenvalue problem for linear Hamiltonian systems of ordinary differential equations. In particular, it is proved that, under certain assumptions, every eigenvalue is isolated and there exists an eigenvalue with any prescribed index.

Key words: Hamiltonian system of ordinary differential equations, nonlinear eigenvalue problem, eigenvalue.

UDC: 519.624.2

Received: 10.10.2006